President Barack Obama seemed to use the authority of his office to put Republican challenger Mitt Romney on his heels in their final presidential debate Monday night, telling Romney he didn't understand foreign policy problems as well as he does.

That idea underlaid some of the night's harshest lines from Obama. He scoffed at Romney's assertion that Russia remained the country's chief geopolitical foe: “The 1980s are now calling to ask for their foreign policy back.”

And when Romney asserted that the United States had fewer naval ships than decades ago, Obama retorted that his opponent didn't understand the modern navy. There were fewer ships, he said, but also fewer “horses and bayonets.”

“We have these things called aircraft carriers, where planes land on 'em,” Obama said. “The question is not a game of battleship, where we're counting ships.”

Romney, for his part, returned to a criticism that Obama had been a weak and indecisive actor on the world stage. He said Obama had shown vulnerability to bad actors around the world and had done too little to support movements for freedom in places such as Iran.

“Nowhere in the world, the influence of America is greater than it was four years ago,” Romney said.

But Romney also took a notably softer and more conciliatory tone than he had in the past, stressing at several points his desire for peace in the world.

“I want to see peace. I want to see growing peace in this country as our objective,” he said in his closing statement. “Promote principles of peace, to make the world a safer place.”

He also picked up a theme of bipartisanship, with words that might have come from Obama's let's-fix-Washington campaign four years ago. “We've got to have a president who can work across the aisle,” Romney said.

“Washington is broken. I know what it takes to get this country back.”

At several points, Romney conceded that he would have done some of the same things that Obama did. He said he would also have instituted economic sanctions against Iran but would have started them earlier. He supported Obama's urging that Egyptian President Hosni Mubarak leave office, but would have urged Mubarak to adapt earlier.

Romney said he also would have supported the military mission that killed Osama bin Laden in Pakistan. And he agreed with Obama's use of unmanned drone strikes to kill suspected terrorists overseas: “I support that entirely and feel the president was right.”

The debate veered at times away from its foreign policy theme.

A question about his plans to pay for a military expansion led Romney to talk about repealing Obama's health care plan.

Obama engaged, with a point about education that also had nothing obvious to do with foreign policy.

The debate began with an exchange about Libya in which the candidates seemed to trade places.

Romney seemed to attack Obama's policy as, in effect, too warlike, saying Obama had focused too much on killing enemies and too little on softer uses of American power.

“We can't kill our way out of this mess” in the Middle East, Romney said.

Obama, by contrast, defended a military solution he used in Libya last summer, organizing an international air campaign that helped defeat Moammar Gadhafi.

He attacked Romney for exactly what Romney had attacked him for before: vagueness and indecision in matters of foreign policy.

“I have to tell you that your strategy, previously, is one that has been all over the map,” Obama said. “And is one that is not designed to keep Americans safe.”

The confrontational tone of the first two debates also returned: this time, initiated first and more forcefully by Obama.

At one point, he told Romney, “Every time you've offered an opinion, you've been wrong” on recent foreign policy matters.

Romney retorted that the criticisms weren't enough: “Attacking me is not an agenda.”